Method of identifying predictive lateral load transfer ratio for vehicle rollover prevention and warning systems

ABSTRACT

A method for controlling stability of a vehicle includes the steps of determining a predictive lateral load transfer ratio of the vehicle by evaluating vehicle performance factors over a period of time, and controlling operation of the vehicle based on the predictive lateral load transfer ratio.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional PatentApplication Ser. No. 60/797,165, which was filed on May 3, 2006 and isincorporated herein by reference in its entirety.

BACKGROUND OF THE DISCLOSURE

Vehicle rollover has the highest fatality rate among non-collisionvehicle accidents. To prevent vehicle rollover, a rollover index calledLateral Load Transfer Ratio (LTR) has been used to detect vehiclerollover propensity. Typically, LTR is estimated from vehicleinformation measured at a fixed point in time. In analogy, it is liketaking a snap-shot of a dynamic system and using this information(frozen in time) to determine the vehicle rollover threat. If thethreshold of the LTR is set to be too low, it will give a warning orprematurely activate the vehicle rollover prevention system duringnormal driving. If the threshold is set to be too high, it may be toolate to prevent the vehicle from rollover. Determining the LTR thresholdis difficult due to dynamic changes in vehicle operation or unexpecteddisturbances, which cannot be captured using only static LTR.

BRIEF SUMMARY OF THE INVENTION

A method for controlling stability of a vehicle is provided thatincludes the steps of determining a predictive lateral load transferratio of the vehicle by evaluating vehicle performance factors over aperiod of time, and controlling operation of the vehicle based on thepredictive lateral load transfer ratio. In an embodiment of theinvention, the predictive lateral load transfer ratio may be used todetect the rollover propensity of a vehicle prior to the vehicleoperating in a condition that induces vehicle rollover. With thisprediction capability, operation of a vehicle rollover warning systemmay be improved to provide a vehicle operator with advanced warning ofan impending rollover. Moreover, a rollover prevention system, includingtorque-biasing devices such as electronic limited-slip differentials,may be operated to prevent vehicle rollover.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of an exemplary all-wheel-drivevehicle employing a vehicle stability control system according to anembodiment of the present invention;

FIG. 2 is a schematic illustration of a vehicle stability control systemaccording to an embodiment of the present invention;

FIG. 3 is a model of vehicle dynamics during lateral operation; and

FIG. 4 is a model of vehicle dynamics during vehicle roll.

DETAILED DESCRIPTION

Referring now to the drawings, which are not intended to limit theinvention, FIG. 1 schematically illustrates an exemplary all-wheel-drivevehicle 20 including a laterally-positioned engine 22. The engine 22 islinked to a pair of front wheels 24 a, 24 b through a front axle ortransaxle 26 and to a pair of rear wheels 28 a, 28 b through a rear axle30. The front axle 26 is primarily and directly driven by the engine 22.The rear axle 30 is indirectly driven via a power transfer unit (notshown) and a center coupling apparatus or coupler 32. The rear axle 30is mechanically linked to the front transaxle 26 through one or moredrive- or prop-shafts. An optional electronically controlled limitedslip differential (ELSD) 34 is used to bias the rear prop-shaft torqueto the rear wheels 28 a, 28 b. Coupler 32 and ELSD 34 may be well knowndevices in the art, and may be controlled by a vehicle control system 58(shown in FIG. 2), such as a vehicle electronic control unit (ECU) orother controller. It will be appreciated that vehicle 20 is not limitedto the configuration shown in the drawings and may include otherconfigurations, including, without limitation, two-wheel driveconfigurations.

As shown in FIG. 2, the control system 58 may include a control unit 60,such as a microprocessor-based ECU including a memory device havingstored therein, for example, one or more maps containing vehicleoperating parameter information, and at least one vehicle sensor 62 formeasuring a vehicle performance factor(s), such as, without limitation,a yaw rate sensor, wheel speed sensor, lateral acceleration sensorand/or a steering angle sensor. The control unit 60 provides an inputsignal to the center coupler 32 and/or the ELSD 34 to control engagementand disengagement of the devices to distribute torque between the wheelsor axles. The control unit 60 may also control operation of a rollwarning device 64, such as, for example, and audible warning device orvisual indicator in the vehicle dash, to warn a vehicle operator of animpending vehicle rollover.

Referring now to FIGS. 3 and 4, the vehicle LTR may be determined fromvehicle nonlinear models as:

$\begin{matrix}{{LTR}:=\frac{F_{zL} - F_{zR}}{F_{zL} + F_{zR}}} & (1)\end{matrix}$

Taking into account the lateral dynamics of the vehicle:

$\begin{matrix}{{{m\overset{.}{v}} = {F_{yrl} + F_{yrr} + {\left( {F_{xfl} + F_{xfr}} \right)\sin\;\delta} + {\left( {F_{yfl} + F_{yfr}} \right)\cos\;\delta} - {mru} + {{mg}\mspace{11mu}\sin\;\phi_{r}} - {{mh}\mspace{11mu}\sin\;{\overset{.}{\phi}}_{v}r^{2}} - {{mh}\;\phi_{v}^{2}\sin\;\phi_{v}} + {{mh}\mspace{11mu}\cos\;\phi_{v}{\overset{¨}{\phi}}_{v}}}}{or}{{{mv} + {mru} - {{mg}\mspace{11mu}\sin\;\phi_{r}} + {{mh}\mspace{11mu}\sin\;\phi_{v}r^{2}} + {{mh}\;{\overset{.}{\phi}}_{v}^{2}\sin\;\phi_{v}} - {{mh}\mspace{11mu}\cos\;\phi_{v}{\overset{¨}{\phi}}_{v}}} = {{mA}_{y} = {{F_{yrl} + F_{yrr} + {\left( {F_{xfl} + F_{xfr}} \right)\mspace{11mu}\sin\;\delta} + {\left( {F_{yfl} + F_{yfr}} \right)\mspace{11mu}\cos\;\delta}} = {\sum F_{y}}}}}} & (2)\end{matrix}$wherein m is the vehicle mass, {dot over (v)} is the vehicle lateralvelocity, r is the vehicle yaw rate, u is the vehicle longitudinalvelocity, g is the acceleration of gravity, A_(y) is the vehicle lateralacceleration, and h is the height of the center of gravity relative tothe vehicle rotational point as shown in FIG. 4.

Taking into account the roll dynamics of the vehicle:

$\begin{matrix}{{\left( {I_{xx} + {{mh}^{2}\sin^{2}\phi_{v}}} \right)\left( {{\overset{¨}{\phi}}_{v} - {\overset{¨}{\phi}}_{r}} \right)} = {{\left( {F_{zL} - F_{zR}} \right) \cdot \frac{T}{2}} + {\sum\;{F_{y} \cdot h_{R}}} + {{\left( {{m\overset{.}{v}} + {mru}} \right) \cdot h}\;\cos\;\phi_{v}} + {{{mg} \cdot h}\;\sin\;\phi_{v}\cos\;\phi_{r}} - {{{mg} \cdot h}\;\cos\;\phi_{v}\sin\;\phi_{r}} + {\left\lbrack {\left( {I_{yy} - I_{zz}} \right) - {mh}^{2}} \right\rbrack{r^{2} \cdot {\sin\left( {{\overset{.}{\phi}}_{v} - {\overset{.}{\phi}}_{r}} \right)}}{\cos\left( {{\overset{.}{\phi}}_{v} - {\overset{.}{\phi}}_{r}} \right)}}}} & (3)\end{matrix}$

Taking into account the vertical dynamics of the vehicle:m{umlaut over (z)}=m({dot over (φ)}_(v) ² h cos φ_(v)+{umlaut over(φ)}_(v) h sin φ_(v))=(F _(zL) +F _(zR))−mg cos φ_(r)  (4)wherein {umlaut over (z)} is the vehicle vertical acceleration.

Accordingly, taking into account equations (1)-(4), the LTR may beexpressed as follows:

${LTR} = {\frac{2}{T}\frac{\begin{matrix}\begin{matrix}{{\overset{.}{\left( {I_{xx} + {{mh}^{2}\sin^{2}\phi_{v}}} \right)}\left( {{\overset{¨}{\phi}}_{v} - {\overset{¨}{\phi}}_{r}} \right)} - {m\;{A_{y} \cdot h_{R}}} +} \\{{m\; A_{y\; 2}h\;\cos\;\phi_{v}} - {m\;{g \cdot h}\;\sin\;\phi_{v}\cos\;\phi_{r}} + {m\;{g \cdot}}}\end{matrix} \\{{h\;\cos\;\phi_{v}\sin\;\phi_{r}} - {\left\lbrack {\left( {I_{yy} - I_{zz}} \right) - {mh}^{2}} \right\rbrack{r^{2} \cdot}}} \\{{\sin\left( {{\overset{.}{\phi}}_{v} - {\overset{.}{\phi}}_{r}} \right)}{\cos\left( {{\overset{.}{\phi}}_{v} - {\overset{.}{\phi}}_{r}} \right)}}\end{matrix}}{{m\left( {{{\overset{.}{\phi}}_{v}^{2}h\;\cos\;\phi_{v}} + {{\overset{¨}{\phi}}_{v}h\;\sin\;\phi_{v}}} \right)} + {m\; g\mspace{11mu}\cos\;\phi_{r}}}}$wherein I_(xx), I_(yy) and I_(zz) are the moments of inertia about x, yand z axis respectively, and whereinA _(y) ={dot over (v)}+ru−g sin φ_(r) +h sin φ_(v) r ² +h{dot over (φ)}_(v) ² sin φ_(v) −h cos φ_(v){umlaut over (φ)}_(v), and A _(y2) ={dotover (v)}+ru.

For relatively small values of φ_(v), {dot over (φ)}_(v), {umlaut over(φ)}_(v), {dot over (φ)}_(r), {umlaut over (φ)}_(r), the LTR may then beexpressed as:

$\begin{matrix}{{{LTR} = {\frac{2}{T} \cdot \frac{{{- {mA}_{y\; 2}} \cdot \left( {h_{R} + h} \right)} + {{{mg} \cdot h_{R}}\sin\;\phi_{r}} + {{{mg} \cdot h}\;\sin\;\phi_{r}}}{mg}}}{or}} & (6) \\{{LTR} = {{\frac{2}{T} \cdot \frac{{- A_{y\; 2}} \cdot \left( {h_{R} + h} \right)}{g}} + {{\frac{2}{T} \cdot \left( {h_{R} + h} \right)}\sin\;\phi_{r}}}} & (7)\end{matrix}$

For a small φ_(r), the LTR may be further estimated as:

$\begin{matrix}{{LTR} = {\frac{2}{T} \cdot \frac{{- A_{y\_ meas}} \cdot h_{CG}}{g}}} & (8)\end{matrix}$wherein, A_(y) _(—) _(meas) is the lateral acceleration, which may beobtained using an accelerometer, and h_(CG) is the total vehicle centerof gravity (CG) height.

In accordance with an embodiment of the present invention, a method fordetermining LTR of a vehicle is provided that includes a predictive LTR(PLTR), which evaluates vehicle performance factors over a period oftime, rather than a fixed point in time. The method is designed toaccurately “count-down” toward rollover or evaluate vehicle performanceprior to rollover under a wide range of vehicle operating conditions.Derivation of PLTR is shown as follows:

$\begin{matrix}{{{PLTR}_{t_{0}}\left( {\Delta\; t} \right)} = {{{LTR}\left( t_{0} \right)} + {L\overset{.}{T}{{R\left( t_{0} \right)} \cdot \Delta}\; t}}} & (9) \\{{{PLTR}_{t_{0}}\left( {\Delta\; t} \right)} = {{\frac{2}{T} \cdot \frac{{A_{y\_ meas}\left( t_{0} \right)} \cdot h_{CG}}{g}} + {{\frac{2}{T} \cdot \frac{h_{CG}}{g}}\frac{\mathbb{d}}{\mathbb{d}t}{\left( A_{y\_ meas} \right) \cdot \Delta}\; t}}} & (10)\end{matrix}$wherein A_(y) _(—) _(meas) is the measured vehicle lateral acceleration.

Equation (10) expresses PLTR at time t₀ predicted for a future timehorizon Δt. The effect of the sign of the measured lateral accelerationmay be neglected in this derivation for proof-of-concept purposes. Themeasured lateral acceleration A_(y) _(—) _(meas) in equation (10) istypically noisy and, therefore, it is difficult to obtain a smooth valueafter a derivation. The following filtering technique is used to reducenoise:

$\begin{matrix}{{{PLTR}_{t_{0}}\left( {\Delta\; t} \right)} = {{\frac{2}{T} \cdot \frac{{A_{y\_ meas}\left( t_{0} \right)} \cdot h_{CG}}{g}} + {{\frac{2}{T} \cdot \frac{h_{CG}}{g}}{\left( {{\frac{1}{{\tau\; s} + 1}{\overset{.}{A}}_{y\_ meas}} + {\frac{\tau\; s}{{\tau\; s} + 1}{\overset{.}{A}}_{y\_ meas}}} \right) \cdot \Delta}\; t}}} & (11)\end{matrix}$wherein τ is a time constant.

The measured lateral acceleration can be further estimated from arelationship with the steering angle using a linear model,

$\begin{matrix}{\frac{{\overset{.}{A}}_{y}}{{\overset{.}{\delta}}_{w}} = {{TF}_{Model}(s)}} & (12)\end{matrix}$wherein TF_(Model)(s) is a linear transfer function of the steeringangle and the lateral acceleration based on the linear model, and δ_(w)is an actual average steered wheel angle. By using this model-basedfilter, the noise from the derivation of the lateral acceleration can befiltered out using a low-pass filter. Moreover, driver's steering inputinformation plays an important role in predicting the rollover index dueto the delay of the steering system.

Accordingly, the PLTR is provided as follows:

$\begin{matrix}{{{PLTR}_{t_{0}}\left( {\Delta\; t} \right)} = {{\frac{2}{T} \cdot \frac{{A_{y\_ meas}\left( t_{0} \right)} \cdot h_{CG}}{g}} + {{\frac{2}{T} \cdot \frac{h_{CG}}{g}}{\left( {{\frac{s}{{\tau\; s} + 1}{A_{y\_ meas}\left( t_{0} \right)}} + {\frac{\tau\; s}{{\tau\; s} + 1}{{{TF}_{model}(s)} \cdot s}\;{\frac{1}{{\tau_{sw}s} + 1} \cdot \frac{1}{SR}}{\delta_{d}\left( t_{0} \right)}}} \right) \cdot \Delta}\; t}}} & (13)\end{matrix}$wherein

${\frac{\delta_{w}}{\delta_{d}} = {\frac{1}{SR} \cdot \frac{1}{{\tau_{sw}s} + 1}}},\delta_{d}$is the driver's steering wheel angle, τ_(sw) is the steering first-ordertime constant and SR is the steering ratio.

A filter,

$\frac{s}{{\tau\; s} + 1},$may be used on the measured lateral acceleration and a filter,

${\frac{\tau\; s^{2}}{\left( {{\tau\; s} + 1} \right)\left( {{\tau_{sw}s} + 1} \right)} \cdot {{TF}_{model}(s)}},$may be used on the driver's steering wheel angle. The selected Δt needsto be long enough to cover the rollover prevention system response time.

Unlike more conventional methods of determining LTR, the new method ofdetermining PLTR may be used by control system 58 to control a vehicletorque biasing device (e.g., center coupling 32 and ELSD 34) to improvevehicle stability and inhibit vehicle rollover. In the embodiment shownin FIGS. 1 and 2 for example, the PLTR may be used by controller 60 todetermine when and to what extent to engage the torque biasing devicesto increase yaw damping of the vehicle and prevent vehicle rollover. Forexample, and without limitation, control unit 60 may be configured suchthat center coupler 32 and/or ELSD 34 are operated once the PLTR exceedsa threshold value(s) or the rate of change of PLTR exceeds apredetermined threshold rate. The PLTR may also be used to controloperation of roll warning device 64 to warn a vehicle operator of animpending vehicle rollover. It will also be appreciated that use of thePLTR to control operation of a vehicle torque biasing device or rollwarning device is not limited thereto, and that the PLTR may be used tocontrol other vehicle systems, such as the vehicle brake system or powersteering system, to inhibit vehicle rollover.

The invention has been described in great detail in the foregoingspecification, and it is believed that various alterations andmodifications of the invention will become apparent to those skilled inthe art from a reading and understanding of the specification. It isintended that all such alterations and modifications are included in theinvention, insofar as they come within the scope of the appended claims.

1. A method for controlling stability of a vehicle comprising the stepsof: determining a predictive lateral load transfer ratio (PLTR) of thevehicle by evaluating vehicle performance factors over a period of time,wherein the PLTR reflects the PLTR calculated at a selected point intime t₀ for a future time horizon Δt; and controlling operation of thevehicle based on the PLTR.
 2. The method of claim 1, wherein the vehicleincludes a torque biasing device for controlling the distribution oftorque between a pair of vehicle wheels or between a pair of vehicleaxles, and the step of controlling operation of the vehicle includesengaging the torque biasing device to control torque distributionbetween the pair of vehicle wheels or the pair of vehicle axles.
 3. Themethod of claim 1, wherein vehicle includes a roll warning device, andthe step of controlling operation of the vehicle includes operating theroll warning device to warn a vehicle operator of an impending vehiclerollover.
 4. The method of claim 1, wherein the step of determining thePLTR includes estimating vehicle lateral acceleration from arelationship with a vehicle steering angle using a linear model:${\frac{A_{y}}{\delta_{s}} = {{TF}_{Model}(s)}},$ wherein TF_(Model) (s)is a linear transfer function of the steering angle and the lateralacceleration based on the linear model, and δ_(w) is an actual, averagesteered wheel angle.
 5. The method of claim 1, wherein the determiningstep includes determining the predictive lateral load transfer ratio asfollows:${{PLTR}_{t_{0}}\left( {\Delta\; t} \right)} = {{\frac{2}{T} \cdot \frac{{A_{y\_ meas}\left( t_{0} \right)} \cdot h_{CG}}{g}} + {{\frac{2}{T} \cdot \frac{h_{CG}}{g}}{\left( {{\frac{s}{{\tau\; s} + 1}{A_{y\_ meas}\left( t_{0} \right)}} + {\frac{\tau\; s}{{\tau\; s} + 1}{{{TF}_{model}(s)} \cdot s}\;{\frac{1}{{\tau_{sw}s} + 1} \cdot \frac{1}{SR}}{\delta_{d}\left( t_{0} \right)}}} \right) \cdot \Delta}\; t}}$wherein Δt is the future time horizon,${\frac{\delta_{w}}{\delta_{d}} = {\frac{1}{SR} \cdot \frac{1}{{\tau_{sw}s} + 1}}},\delta_{d}$is a vehicle steering wheel angle, τ_(sw) is a steering first-order timeconstant, and SR is the steering ratio.
 6. The method of claim 5,further including the step of using a filter,$\frac{s}{{\tau\; s} + 1},$ on the measured lateral acceleration andusing a filter,${\frac{\tau\; s^{2}}{\left( {{\tau\; s} + 1} \right)\left( {{\tau_{sw}s} + 1} \right)} \cdot {{TF}_{model}(s)}},$on the driver's steering wheel angle.
 7. The method of claim 5, whereinthe vehicle includes a control system and the determining step includesselecting the future time horizon Δt to be at least as long as thevehicle rollover prevention system response time.